Fluid simulation pours into the cup in a box shape and won't spill
Setting your cup to obstacle (as mentioned in the comment above) should fix the problem of the cup bounds being square. The main thing you would want to fix, though, would be the size of your fluid domain. It will not affect the fluid, but will simulate the bounds of where the fluid will go. A smaller domain will give the waters smaller boundaries. Also, if you are using a rigid body for the cup, it will not simulate well with the fluid.